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Popular >

d/(ds)(s/(s^2+2))

Solution

\frac{d}{d s} (\frac{s}{s ^{2} + 2})

Solution

\frac{- s ^{2} + 2}{( s ^{2} + 2 ) ^{2}}

Solution steps

\frac{d}{d s} (\frac{s}{s ^{2} + 2})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d s}{d s} ( s ^{2} + 2 ) - \frac{d}{d s} ( s ^{2} + 2 ) s}{( s ^{2} + 2 ) ^{2}}

\frac{d s}{d s} = 1

\frac{d}{d s} (s^{2} + 2) = 2 s

= \frac{1 \cdot ( s ^{2} + 2 ) - 2 ss}{( s ^{2} + 2 ) ^{2}}

1 \cdot (s^{2} + 2) - 2 ss = - s^{2} + 2

= \frac{- s ^{2} + 2}{( s ^{2} + 2 ) ^{2}}

Popular Examples

limit as x approaches-1 of 3/(x+1)

x \to - 1 lim (\frac{3}{x + 1})

integral from 0 to 1 of sin(2x)

\int_{0}^{1} sin (2 x) d x

limit as x approaches 0 of 1/(ln(1+x))-1/x

x \to 0 lim (\frac{1}{ln ( 1 + x )} - \frac{1}{x})

integral of 12xsec^2(x)

\int 12 x sec^{2} (x) d x

(\partial)/(\partial y)((x+2y^3)^{1/3})

\frac{\partial}{\partial y} ((x + 2 y^{3})^{\frac{1}{3}})

Frequently Asked Questions (FAQ)

What is the d/(ds)(s/(s^2+2)) ?
The d/(ds)(s/(s^2+2)) is (-s^2+2)/((s^2+2)^2)
What is the first d/(ds)(s/(s^2+2)) ?
The first d/(ds)(s/(s^2+2)) is (-s^2+2)/((s^2+2)^2)